I understand the general approach; my response was to this concrete budget-based proposal. However, you say:
There’s arbitrariness in the choice of questions, but it’s not quite as arbitrary as you think.
It is in fact extremely arbitrary. You’re avoiding the arbitrariness necessary for defining a normed vector space of political positions by offloading the same arbitrariness to the choice of questions in this model. Both approaches would likely correctly identify extreme outliers that are far from the mainstream, but the measured amount of variation within clustered groups would be, in both cases, an equally arbitrary reflection of the model author’s preconceptions.
To take an extreme example, you could have a hundred questions, ninety of which deal with various intricacies of Christian theology, while the rest deal with human universals. If you administered them to a representative sample of the world’s population, your model would tell you that the opinions of Christians span a much wider range of views than the opinions of non-Christians. The same principle applies—perhaps less obviously, but no less powerfully—to any other conceivable questionnaire.
This comment (I think) makes your point clearer to me. The problem isn’t so much in the “send your directed graph to a metric space” as it is “choose a basis of your metric space.”
I think there is a sense in which you could find “less arbitrary” choices, but I don’t think an algorithm exists among humans to find one reliably so I think you’re right.
I understand the general approach; my response was to this concrete budget-based proposal. However, you say:
It is in fact extremely arbitrary. You’re avoiding the arbitrariness necessary for defining a normed vector space of political positions by offloading the same arbitrariness to the choice of questions in this model. Both approaches would likely correctly identify extreme outliers that are far from the mainstream, but the measured amount of variation within clustered groups would be, in both cases, an equally arbitrary reflection of the model author’s preconceptions.
To take an extreme example, you could have a hundred questions, ninety of which deal with various intricacies of Christian theology, while the rest deal with human universals. If you administered them to a representative sample of the world’s population, your model would tell you that the opinions of Christians span a much wider range of views than the opinions of non-Christians. The same principle applies—perhaps less obviously, but no less powerfully—to any other conceivable questionnaire.
This comment (I think) makes your point clearer to me. The problem isn’t so much in the “send your directed graph to a metric space” as it is “choose a basis of your metric space.”
I think there is a sense in which you could find “less arbitrary” choices, but I don’t think an algorithm exists among humans to find one reliably so I think you’re right.
That’s certainly true. The choice of questions is entirely subjective.